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TSR Wiki > Study Help > Subjects and Revision > Revision Notes > Mathematics > Vectors

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Contents 1 Vectors 2 Multiplication by a Scalar 2.1 Example 3 Vector Manipulation 3.1 Example 3.2 Example 4 Unit Vectors 4.1 Example 5 Comments

Vectors

A vector quantity has both length (magnitude) and direction. The opposite is a scalar quantity, which only has magnitude. Vectors can be denoted by AB, a, or AB (with an arrow above the letters).

If:

then the vector will look as follows:

(Diagram missing)

NB1: When writing vectors as one number above another in brackets, this is known as a column vector.

NB2: in textbooks and here, vectors are indicated by bold type. However, when you write them, you need to put a line underneath the vector to indicate it (i.e. a).

Multiplication by a Scalar

When multiplying a vector by a scalar (i.e. a number), multiply each component of the vector by the scalar.

Example

If , and , sketch a and b.

If , .

(Diagram missing)

Vector Manipulation

(Diagram missing)

Example

If If and If , find the magnitude of their resultant.

The resultant of two or more vectors is their sum.

The resultant therefore is .

The magnitude of this is .

The addition and subtraction of vectors can be shown diagrammatically. To find a + b, draw a and then draw b at the end of a. The resultant is the line between the start of a and the end of b.

To find a - b, find -b (see above) and add this to a.

Example

(Diagram missing)

Unit Vectors

A unit vector has a magnitude of 1. The unit vector in the direction of the x-axis is i and the unit vector in the direction of the y-axis is j. For example on a graph, 3i + 4j would be at (3 , 4). This method is another method of writing down vectors.

Example

(3i + j) + (5i - 4j) = 8i - 3j.

This is equivalent to:

.

Comments